Corporate control and executive selection
Francesco LippiUniversity of Sassari and EIEF
Fabiano Schivardi LUISS and EIEF
In firms with concentrated ownership the controlling shareholder may pursue nonmonetary private returns, such as electoral goals in a firm controlled by politi-cians or family prestige in family firms. We use a simple theoretical model to ana-lyze how this mechanism affects the selection of executives and, through this, the firm’s productivity compared to a benchmark where the owner only cares about the value of the firm. We discuss identification and derive two structural estimates of the model, based on different sample moments. The estimates, based on a matched employer–employee data set of Italian firms, suggest that private returns are larger in family- and government-controlled firms than in firms controlled by a conglomerate or by a foreign entity. The resulting distortion in executive selec-tion can account for total factor productivity differentials between control types of up to 10%.
Keywords. Corporate governance, private returns, total factor productivity. JELclassification. D2, G32, L2.
1. Introduction
This paper studies executive selection in firms with concentrated ownership, a con-trol structure that the recent corporate finance literature has shown to be very diffused around the world (La Porta, Lopez-de-Silanes, and Shleifer (1999), Faccio and Lang (2002)). Unlike public corporations, where the separation between ownership and trol naturally puts agency issues at center stage, our hypothesis is that in firms with con-centrated ownership, the controlling shareholder may pursue nonmonetary private re-turns such as electoral goals in a firm controlled by politicians or family prestige in a firm Francesco Lippi:f.lippi@uniss.it
Fabiano Schivardi:fschivardi@luiss.it
We thank the editor and three anonymous referees for useful and constructive criticisms. We are also grate-ful to Fernando Alvarez, Gadi Barlevy, Marco Bassetto, Jeff Butler, Jeff Campbell, Hugo Hopenhayn, Mari-acristina De Nardi, Giuseppe Moscarini, Tommaso Nannicini, Marco Pagano, Ariel Pakes, Mark Roberts, Bernard Salanié, Yossi Spiegel, Andy Skrzypacz, Luke Taylor, Nicholas Trachter, Francis Vella, and seminar participants at EIEF, University of Sassari, Tor Vergata University, Catholic University in Milan, University of Bologna, Georgetown University, the SED meetings, the CEPR–Bank of Italy conference on “Corporate Gov-ernance, Capital Structure and Firm Performance,”and the Federal Reserve Bank of Chicago. This paper is dedicated to the executives who build a career on competence rather than on compliancy and networking. Copyright © 2014 Francesco Lippi and Fabiano Schivardi. Licensed under the Creative Commons Attribution-NonCommercial License 3.0. Available athttp://www.qeconomics.org.
controlled by an individual.1We focus on a specific form of owners’ private benefits: we assume that owners may derive utility not only from profits, but also from employing executives with whom they have developed personal ties. Personal ties and repeated interaction can facilitate the delivery of nonmonetary payoffs that are typically not ver-ifiable in court and therefore cannot be part of the employment contract. For example, the owner of a family business might enjoy a compliant entourage and/or a group of ex-ecutives who pursue family prestige, possibly at the expense of the value of the firm.2If owners value personal ties, they might do so at the expenses of managerial ability, thus distorting the process of executive selection with respect to a situation where the owner only aims to maximize the value of the firm. We formalize this mechanism and propose two distinct sets of structural estimates to quantify its effects on firms’ productivity.
We consider a simple partial-equilibrium, infinite horizon economy in which the firm owner chooses the firm’s executives. We assume that average managerial ability de-termines the firm total factor productivity (TFP).3 Executives are heterogeneous along
two dimensions: their ability (productivity) and their relationship value. The owner only learns these values after an in-office trial period for the executive. Upon learning ability and relationship value, the owner decides whether to give tenure to the executive, who in this case turns “senior,” or to replace him with a “junior” one. We assume that rela-tionship building takes time, so that only senior executives may deliver private returns from the personal relationship. The key decision for the firm owner is whether to retain the executive in the firm after the trial period or to replace her with a junior one. Once tenured, executives in office die with an exogenous probability.
The model is formulated as an optimal sequential search problem in the spirit of McCall (1970)andWeitzman (1979). We solve it analytically and derive three key predic-tions that form the basis for our empirical investigation. First, the firm’s productivity de-clines monotonically with the importance assigned to private benefits. This is because the owner’s tenure decisions are based less on ability and more on personal ties as the importance of private benefits increases. Second, the owners who attach more impor-tance to relationships will, on average, retain a larger share of senior executives, as some low-ability executives with whom they have developed a personal relationship will not be fired. Finally, we show that the cross-firm correlation between productivity and the share of senior executives measures the strength of the selection effect on managerial ability, defined as the difference in the average ability of senior and junior executives. 1Consistent with the hypothesis that control commands a premium,Dyck and Zingales (2004)provided
cross-country evidence that controlling blocks are sold on average at a 14% premium, up to 65% in cer-tain countries; see below for more details. The importance of private benefits of control is also stressed byMoskowitz and Vissing-Jørgensen (2002), who showed that in the United States, average returns of pri-vately held firms are dominated by the market portfolio. They concluded that owners of private firms must be obtaining some form of nonmonetary return.
2Becker was the first to stress the importance of nonpure consumption components of preferences for
individual decision making, for example, in his classic analysis of discrimination (Becker (1971)). In the introduction to the book that collects his contributions on this topic, he stated that “Men and women want respect, recognition, prestige, acceptance, and power from their family, friends, peers, and others” (Becker
(1998, p. 12)).
Intuitively, if selection is based on talent only, then a large fraction of senior executives signals that the firm found a talented pool of executives and is, therefore, highly pro-ductive. Instead, when the owner cares mostly about personal ties, a large share of se-nior executives is not very informative about the firm’s productivity, because their ability played little role in the selection process. We prove that this correlation can be estimated by an ordinary least squares (OLS) regression of TFP on the share of senior executives.
The empirical analysis is based on a sample of Italian manufacturing firms for which we have detailed information on the firms’ characteristics, including the complete work history of their executives. We construct TFP using theOlley and Pakes (1996) proce-dure, and define senior executives as those who have been with the firm for at least 5 years. The data classify the controlling shareholder into four broad control types: in-dividual/family, the government, a conglomerate, or a foreign/institutional owner. We estimate the model by allowing the importance of private returns to vary across control types (conditional on additional covariates, such as time and sectoral effects).
Our first exercise is based on measuring the selection effect via an OLS regression of TFP on the share of senior executives. We find that selection is weaker in government and family firms, and that private benefits generate substantial losses in productivity. Note that these estimates are not based on differences in average productivity and se-niority across types, as we include ownership dummies. Still, omitted variables and un-observed heterogeneity might give rise to the correlation we observe within type. For example, one might conjecture that older firms might both be more productive and em-ploy more senior executives. We address this important criticism in two ways. First we argue, and show formally, that the omitted variable bias might explain the correlation within type, but not the differences across types. It is precisely the variation of the es-timated coefficients across types that is predicted by our model and confirmed by the data. Second, we perform a large series of robustness checks, such as adding more con-trols and using profitability—rather than productivity—as a performance indicator.
We then move on to a structural estimation of all the model parameters. We show that there is a one-to-one mapping between the average productivity and seniority mea-sured in the data, and the model parameters that capture the importance of private ben-efits. We find that the executive selection is distorted with respect to the benchmark of no private benefits in all control types. The distortion is smallest for conglomerate and foreign-controlled firms. Private benefits account for a decrease in average firm produc-tivity of around 6% in family firms and of 10% in government firms, as compared to conglomerate- and foreign-controlled firms. Compared to the theoretical benchmark of no private benefits, productivity losses are on the order of 7% for conglomerates, 8% for foreign firms, 13% for family firms, and 17% for government firms.
We finally compare the OLS and the structural estimates. This comparison is in-formative because the two sets of estimates use different sources of data variability to identify the parameters: within-type correlation in productivity and seniority for the OLS, and variation in average sample moments across control types for the structural estimates. Nothing in the estimation procedure imposes that the two sets of estimates should be consistent. The fact that they do produce quantitatively similar results offers further support for the mechanism we propose.
Two important caveats should be kept in mind. First, our empirical analysis is based on a set of joint predictions: on the degree of correlation between TFP and seniority within an ownership type, as well as on the correlation of average TFP and average seniority across ownership types. These patterns are explained in terms of differences in the degree of private benefits. Of course, firms with different ownership types differ along other aspects. Arguably, one can think of alternative mechanisms that can explain each specific pattern we find in the data. However, the advantage of a formal model is that it supplies an explicit and coherent framework that accounts for all these facts simultaneously and allows us to assess their consistency, as well as their impact on pro-ductivity via counterfactuals, in a quantitative way. Second, we cannot draw normative implications from our analysis, as private benefits do enter the owners’ utility function. We only stress that they come at a cost in terms of productivity.
The paper is organized as follows. The next section discusses the connection with the literature, in particular withAlbuquerque and Schroth (2010), Bandiera, Guiso, Prat, and Sadun (forthcoming), andTaylor (2010), who studied related problems. Section3 develops a model to study how the presence of private returns affects the selection of executives and average productivity within a firm. Section4describes the matched employer–employee data and the classification of the various types of corporate con-trol. In Section5, we study the mapping between the model and the data, discussing the identification of the structural model parameters. Section6presents a test of the model hypotheses that exploits a model-based regression analysis. A subsection discusses sev-eral robustness checks and alternative hypotheses. Section7presents structural esti-mates of the model parameters, which are used to quantify the “costs” of private benefits in terms of foregone productivity by means of simple counterfactual analysis. Section8 concludes.
2. Related literature
The idea that private benefits play a central role in shaping firms’ performance is cen-tral to the recent corporate governance literature La Porta, Lopez-de-Silanes, Shleifer, and Vishny (2000).Dyck and Zingales (2004)empirically estimated the value of private benefits of control using the difference between the price per share of a transaction that involved a controlling block and the price on the stock market before that transaction. They found large values of private benefits of control. In particular, at 37%, the value of private benefits in Italy is the second highest in a sample of 39 countries. Compared to this literature, we focus on a very specific channel through which the private bene-fits arise: the relationship between the owner and her executives. Moreover, we use the model’s predictions on productivity and executive seniority distribution to estimate the value of such a relationship, rather than referring to stock market data.
In our model, the inefficient selection occurs because the firm owner assigns value to the personal relationship with the executives. The fact that personal ties between firms’ high-ranked stakeholders (large shareholders, board members, top managers) is detrimental for firm performance finds support in recent literature.Bandiera, Barankay, and Rasul (2009)studied the effects of social connections among managers and work-ers on performance. Using a field experiment, they showed that managwork-ers favor workwork-ers
who they are socially connected to, possibly at the expense of the firm’s performance. Kramarz and Thesmar (2013) studied the effects of social networks on the composi-tion of firms’ boards of directors and performance in France. They found that networks, defined in terms of school of graduation, influence the board composition; moreover, firms with a higher share of directors from the same network have a worse performance. Battistin, Graziano, and Parigi (2012)studied the effects of connections of top executives in Italian banks on bank performance and turnover. Consistent with our results, they concluded that connections reduce turnover and worsen performance, particularly in local banks.
Our work also relates to the vast body of literature that documents that firms of very different productivity levels coexist even within narrowly defined markets (see, e.g., Bartelsmann and Doms (2000),Syverson (2011)). As inLucas (1978), in our model, dis-persion in firm productivity derives from the underlying disdis-persion in managerial abil-ity, subject to a cutoff level dictated by the selection effect.4Differently from Lucas, in our model, owners are willing to accept a low return on their investment because they derive other types of returns, which weakens the selection effect and increases the cross sectional dispersion in firms productivity. Empirically, we find this to be more relevant for family firms, in line with a growing literature on empirical work practices and per-formance in family firms (see, for example,Moskowitz and Vissing-Jørgensen (2002), Bloom and Van Reenen (2007),Bandiera et al. (forthcoming),Michelacci and Schivardi (2013)).
In terms of managerial turnover,Volpin (2002)studied top executive turnover in Ital-ian listed firms. Consistent with our findings, family-controlled firms tend to have lower turnover rates than foreign-controlled firms.5Executive compensation, promotion poli-cies, and turnover are subject to a growing and heterogeneous body of model-based empirical analysis, using, among others, assignment (Gabaix and Landier (2008),Terviö (2008)) or moral hazard models (Gayle, Golan, and Miller (2009)). Compared to this liter-ature, we do not explicitly formalize the market for executives, but focus on the owner’s decision to confirm or replace incumbent executives.
Three recent papers are closely related to ours. Albuquerque and Schroth (2010) used a structural model to estimate the private benefits of control in negotiated block transactions. They found evidence consistent with the hypothesis that those benefits are large.Taylor (2010)built and estimated a structural model of chief executive officer (CEO) turnover with learning about managerial ability and costly turnover. He found that only very high turnover costs can rationalize the low turnover rate observed in the data.6He interpreted this result in terms of CEO entrenchment and weak governance.7
4Heterogeneity in an underlying unobservable firm characteristic has become the standard way to model
productivity dispersion at the firm level both in industrial organization (IO) (Jovanovic (1982),Hopenhayn (1992),Ericson and Pakes (1995)) and in trade (Bernard, Eaton, Jensen, and Kortum (2003),Melitz (2003)).
5He also found that the sensitivity of turnover to performance, an indicator of the quality of the
gover-nance, is not significantly different in the two groups. However, his sample has a small number of foreign-controlled firms and, in fact, his main analysis is focussed on family-foreign-controlled firms only.
6See alsoTaylor (2013)for a model of learning about CEOs’ ability and wage dynamics.
7Garrett and Pavan (2012)studied managerial turnover when the quality of the match between a firm and
Compared to his paper we propose a different, possibly complementary, reason for in-efficient turnover: owners trade off efficiency for the private benefits of the personal relationships with their executives. We also use data on all top executives, rather than CEOs alone, and exploit different ownership structures to estimate our model parame-ters.Bandiera et al. (forthcoming)analyzed the role of incentive schemes in family and nonfamily firms, assuming that family firms pursue private benefits of control. They showed that family firms rely less on performance-based compensation schemes and attract more risk-averse and less able managers. The model predictions are supported by reduced-form regressions. We see their paper and ours as complementary. In fact, Bandiera et al. (forthcoming)focussed on the optimal compensation scheme, an issue that is ignored in our model. On the other hand, we introduce learning about managerial ability in a dynamic setting, so that we can study turnover and seniority composition. Moreover, we provide direct structural estimates of the importance of private benefits by control type, supplying supporting evidence for a central assumption of their model.
3. Amodel of executive tenure and firm productivity
We model the decision problem of a firm owner in charge of selecting the executives who run the firm. Our aim is to use the model to organize the empirical analysis. Given that we will structurally estimate the model parameters, we keep it as simple as possible. In particular, we focus on the owner’s selection problem and completely put aside the market for executives.8A firm employs n executives, depending on its size (not modeled here). Each executive is characterized by an ability level xi. We assume that ability is a shifter of the production function, ¯xF(K L), where ¯x =n1ixiis the average manage-rial ability, K is the capital stock, and L is labor. This assumption has two consequences. First, it implies that we will be able to measure average managerial ability by firm-level TFP, which we use in the empirical section. Second, the fact that overall TFP is additive in individual ability implies that we can study the problem of the owner for each single executive in isolation from the others, as we exclude spillovers in ability among them. This greatly simplifies the analysis in the model that we present next. We also assume that, conditional on ¯x, K and L are chosen optimally so that the profit function can be written only as a function of ¯x, and capital and labor can be ignored in what follows without loss of generality.
3.1 The model
The problem describes executive selection by the firm owner. The executives are hired at the junior level and become senior—and eligible for tenure—after one period. We think of this period as the time during which executive’s quality is learned by the owner. An that the optimal retention decision becomes more permissive over time, offering an alternative explanation for what would look like CEO entrenchment.
8Our conjecture, to be verified in future work, is that the effects we identify would also hold both in a
competitive market for executives and in a search framework. In fact, as long as the private benefits create a surplus, they should affect executive selection in the same way as in our framework, independently from the surplus splitting rule.
executive’s quality is characterized by two independent exogenous variables: his pro-ductivity x, a nonnegative random variable with continuous and differentiable cumula-tive distribution function (CDF) G(x) with G(0)= 0 and expected value μ =0∞x dG(x), and his relationship value r, a nonnegative random variable that is identically zero for a junior executive and equals zero with probability 1− q or equals R with probability q for a senior executive. The personal relationship is valuable because it facilitates the de-livery of nonmonetary payoffs, which cannot be explicitly included in an employment contract. For example, a politician might value executives who serve his political inter-ests in government-controlled firms by hiring workers in his constituency. The owner of a family business might enjoy a compliant entourage and/or a group of executives who pursue the prestige of the family. The rationale for the value of relationships to mature only for senior executives is that relationships take time to develop.9
We assume that on hiring a (junior) executive, the owner observes neither x nor r, but only knows their distribution. At the end of the first period, the owner learns the value of the executive’s productivity—a realization of x—and the value of his relationship—the realization of r (either 0 or R > 0). It is assumed that both the exec-utive relationship value and the productivity are specific to an execexec-utive–firm match, so that if an executive moves to a new firm, both his x and r are unknown to the new owner. After learning the realization of x and r, the owner decides whether to keep the executive in office (i.e., give him tenure) or to replace him with a junior one (i.e., fire the incumbent executive). It is convenient to define a new random variable s≡ x + r. Using that x and r are independent, the CDF is
F(s)= qGmax(s− R 0)+ (1 − q)G(s) ∀s > 0 (1) so that the probability that a senior executive with r+ x ≥ s is observed is 1 − F(s).
If appointed, the (senior) executive stays one period with the firm and then dies with an exogenous constant hazard ρ, so that the expected office tenure of a senior executive is 1/ρ. When a senior executive dies, the owner replaces her with a junior one.
The per-period return for the risk-neutral owner is given by the realizations of st= xt+ rt; his utility is given by the expected present value of the sum of these real-izations, v≡∞t=0βtst, where β is a time discount. The owner cares about the executive productivity and his/her relationship value, and decides whether or not to fire an exec-utive after observing the realization of both variables at the end of the first period. When a junior executive is in office at the beginning of period t, there is no further decision to be taken for the owner, and the expected value for the owner is
vy= μ + βE˜smaxvy vo(˜s)
9Of course, personal relationships might develop before the match forms, for example, if an owner hires
friends or relatives. In this case, exactly the same logic would apply to “connected” (friends or relatives) versus “unconnected” executives. Unfortunately, in the data, we have no way to detect this type of relation-ships, while we observe seniority. The two channels of personal ties are not mutually exclusive and might both be at play.
where expectations are taken with respect to the next-period realization of the executive value˜s and vo(˜s) denotes the value of a senior executive with known value ˜s. This value is vo(˜s) = max vy˜s + β ρvy+ (1 − ρ)vo(˜s) (2)
where the value function vo(˜s) is continuous and increasing in ˜s.
The optimal policy follows a threshold rule: the owner fires the senior executive if s < s∗, that is, if the value of s= r + x, learned when the executive becomes senior, is below the threshold s∗.10 To be clear about the condition that pins down the optimal
threshold value s∗, it is useful to introduce two more pieces of notation. Let vy¯sdenote the conditional value of a junior executive under a generic policy threshold¯s. Likewise, let us define vo¯s(˜s) as the conditional value of a senior executive of type ˜s ≥ ¯s under a generic policy threshold¯s. Obviously ¯s enters both (conditional) value functions because it determines the senior executives who will be fired, that is, all those for whom s <¯s. We can now state the condition that defines the optimal value of the threshold s∗ as the smallest value of s that leaves the firm indifferent between keeping the senior executive or appointing a junior one, namely
vos∗s∗= vys∗ (3)
AppendixAshows how equation (3) can be used to obtain an analytical characterization of s∗that is useful for the comparative statics analysis below. This characterization leads us to state our first proposition.
Proposition 1. Given the primitives β, ρ, G(·), and q, there exists a unique optimal threshold s∗(R). Moreover, (i) s∗(0) > μ, (ii) s∗(R)satisfies 0 <∂s ∗(R) ∂R = qβ 1− G(s∗− R) 1+ β(1 − F(s∗))< qβ < 1 See AppendixBfor the proofs of all propositions.
The proposition states that when R≡ 0 (relationships bring no value to the owner), the optimal threshold s∗(0) > μ. Hence the senior executive retains office only if he is sufficiently above the expected value of a junior μ. This is because the appointment of a junior, and the possibility of future replacement, gives the policy of appointing a junior a positive option value. The fact that productivity x is learned after one period induces a selection whereby senior executives who retain office are more productive than the average junior executive. This is shown in Figure1, where the optimal threshold for the R= 0 case lies to the right of μ (the mean of the ability distribution).
10As in theMcCall (1970)model, the proof relies on the fact that the functions v
o(˜s) and vycross only
Figure 1. Example of selection thresholds for R = 0 and R = 5. Note: The figure uses the pa-rameters β= 098 (per year), ρ = 011 (per year), and q = 075; G(·) is log normal with log mean λm= 16 and log std λσ= 036, which imply μ = 53.
The second part of the proposition characterizes how the optimal threshold s∗varies with R. The larger is the importance of the nonmonetary returns to the owner (as mea-sured by a higher value of R), the greater is the value of the threshold s∗. This has two contrasting effects on the productivity of the executives who get tenure. The fact that ∂s∗/∂R < 1implies that as R increases, the productivity threshold for the executives who develop a relationship (i.e., those with r= R) falls, since s∗− R is decreasing in R. On the other hand, the threshold for the executives who do not develop a valuable relationship (i.e., those with r= 0) increases: these executives must compensate for their lack of “re-lationship” value with a higher productivity, such that x≥ s∗. As shown in Figure1, the ability thresholds for executives with and without relationship value, respectively given by s∗− R and s∗, move apart as R increases.
We now turn to the model prediction concerning the seniority composition of the firm’s executives in a steady state. The fraction of senior executives in office, φ, follows the law of motion
φt= φt−1(1− ρ) + (1 − φt−1)1− Fs∗ so that the steady state fraction of senior executives is
φs∗= 1
1+ ρ
1− F(s∗)
which is decreasing in ρ. Mechanically, a lower hazard rate increases the fraction of se-nior executives. It is also immediate that φ is decreasing in F(s∗). To study how φ de-pends on R, we need to compute the total derivative of F(s∗), since changes in R affect the CDF directly and also affect the threshold s∗. Note that
dF(s∗) dR = qgs∗− R+ (1 − q)gs∗ ∂s ∗ ∂R− qg s∗− R (5)
Recall that ∂s∂R∗ < q (see Proposition 1) shows that the derivative is negative at R= 0, which means that at R= 0, the share of senior executives is increasing in R. Intuitively, when R > 0, the appeal of senior executives increases because, all other things equal, their expected return is increased by the expected value of relationships, qR. However, the effect of R on φ cannot be signed, in general, when R > 0, because an increase in R has two opposing effects. On the one hand, it lowers the threshold s∗− R for that frac-tion (q) of senior executives who display valuable relafrac-tionships (r= R); this increases φ. On the other hand, a higher s∗ raises the acceptance threshold for the senior execu-tive with no relationship capital (r= 0); this reduces φ. The final effect thus depends on the features of the distribution of x and r. In fact, when q is sufficiently small and Ris sufficiently large, the option value of searching for an executive who delivers R is high enough to induce a low retention rate.11An example is displayed in the left panel of Figure2.
Figure 2. Share of senior executives and senior–junior differential as R varies. Note: The figure uses the parameters β= 098 (per year), ρ = 011 (per year), and q = 075; G(·) is log normal with log mean λm= 16 and log std λσ= 036, which imply μ = 53.
11It is immediate to show that a decrease in q accompanied by a corresponding increase in R, to keep the
expected value of r fixed, leads to an increase in the variance of r. This, in turn, increases the option value of searching for an executive who delivers the relationship value.
We now analyze how changes in R affect the firm’s average productivity in the steady state. Let X denote the mean productivity of the firm, given by the weighted average of the expected productivity of the junior and senior executives,
Xs∗= Erx(x)= μ + φs∗Xos∗− μ (6) where some algebra shows that the senior executives’ average productivity is
Xo s∗= q ∞ s∗−Rx dG(x)+ (1 − q) ∞ s∗ x dG(x) 1− F(s∗) (7)
This leads us to the next proposition.
Proposition 2. Let β → 1. Then the steady state firm productivity X(s∗)is (i) maximal under the policy s∗(R= 0), with∂X∂R R=0= 0,
(ii) decreasing in R,∂X∂R R>0< 0.
Proposition2shows that the mean productivity of a firm is maximized when the firm only cares about ability, that is, under the policy s∗(R= 0). Any policy s∗(R)with R > 0 induces, on average, a lower firm productivity. Moreover, the proposition shows that X is monotone decreasing in R.12 This will be useful in the discussion of the parameters identification below. The assumption that β→ 1 simplifies the derivation and is useful to interpret the mean X as a cross section average.13 The proposition also establishes that the derivative of X with respect to R is zero at R= 0. This result, and the fact that the share of senior executives is increasing at R= 0 (discussed above), implies that the productivity differential between senior and junior executives, Xo− μ, is decreasing in Rat R= 0, as can be seen from equation (7):
∂{Xo(s∗)− μ} ∂R R=0= g(s∗) q−∂s ∗ ∂R s∗− ∞ s∗ x dG(x) 1− G(s∗) 1− G(s∗) < 0
The intuition behind this pattern is simple: as R increases, the owner selects less on abil-ity, so that the senior executives become more similar to the unselected pool of junior 12One might argue that in a competitive equilibrium, firms whose owners have a large R should not be
able to survive, as they are less efficient than small R firms. This is not necessarily the case. An owner who enjoys a private benefit might be willing to accept a return on assets below the market return, as she is trading off monetary for nonmonetary returns. Of course, she would still need to meet the no-bankruptcy constraint, which is, however, less stringent than matching the market return. This implies that in equi-librium, firms with different R’s—and, therefore, different productivity levels—can coexist. As discussed in the literature review, there is evidence that the return on privately held firms is dominated by the market portfolio (Moskowitz and Vissing-Jørgensen (2002)).
13The numerical analysis of the model for β∈ (085 1) (per year) gives very similar results. The
executives. The right panel of Figure2shows that this pattern holds for a wide set of pa-rameter values and, in particular, for the papa-rameters that are in a (broad) neighborhood of our structural estimates (thick line). The figure also shows that in the parametrization with the high value of q= 075, both φ and Xo− μ become flat functions of R for R ∼= 8: at this point, owners are basically already firing all executives with r= 0 and keeping all those with r= 8, so that further increases in R no longer influence the selection process. In other words, X and φ asymptote to constant values as R grows large. We will come back to this observation when we comment on the results of our estimates.
We conclude this section with a brief discussion of our modeling assumptions about the distribution of abilities. For the sake of simplicity, the model introduced an asymme-try between ability and the relationship value, assuming that only the latter grows with seniority. We notice that this is not a necessary assumption for Proposition2(ii) to hold; what is necessary for this result, even if we allowed ability to evolve with seniority, is that such evolution is uncorrelated with R. Intuitively even if executives become more pro-ductive when turning senior (on average), it would still be the case that owners who are more interested in R will select more based on private benefits and less on productivity. Of course, this result would break down if owners who care more about private ben-efits are also attached to executives whose productivity increases relatively faster with seniority than owners who are not interested in private benefits. This would be the case if such owners, for example, invest more in executive training. Note, however, that in such cases, the relationship between R and productivity could even become positive, an implication we will be able to test (and dismiss) empirically.
4. Data description
In this section, we describe the main features of our data, referring to AppendixDfor more details. The data match a large sample of executives with a sample of Italian firms. The executives represent approximately 2% of the firm’s employment. The firm data are drawn from the Bank of Italy’s annual survey of manufacturing firms (INVIND), an open panel of around 1200 firms per year that is representative of manufacturing firms with at least 50 employees. It contains detailed information on firms’ characteristics, including industrial sector, year of creation, number of employees, value of shipments, value of exports, and investment. It also reports sampling weights to replicate the universe of firms with at least 50 employees. We completed the data set with balance-sheet data collected by the Company Accounts Data Service (CADS) since 1982, from which it was possible to reconstruct the capital series using the perpetual inventory method. All these manufacturing firms belong to the private sector and are, therefore, subject to the same legislation, particularly in terms of labor laws.
Our measure of productivity is TFP. We assume that production takes place with a Cobb–Douglas production function of the form
Yit= TFPitKitβLαit
where Y is value added, K is capital, L is labor, and i, t are firm and year indices, respec-tively. TFP depends on average managerial ability X, and, possibly, on other additional
observable and unobservable characteristics Wit, such as the industrial sector, the firm size, and time effects,
TFPit= 1 nit nit j=1 Xj eWit+ it
where nit is the number of executives in firm i at t, Xj is the ability of executive j= 1 2 nit, and itis an independent and identically distributed (i.i.d.) shock un-observed to the firm or, more simply, measurement error in TFP. We estimate TFP using theOlley and Pakes (1996)approach. The procedure is briefly described in AppendixD; full details are given inCingano and Schivardi (2004).
The survey contains several questions regarding the controlling shareholder. The most relevant for our purpose is “What is the nature of the controlling shareholder?,” from which we construct an indicator that groups firms into one of four control cat-egories (see AppendixDfor the details): (i) individual or family; (ii) government (lo-cal or central or other government controlled entities); (iii) conglomerate, that is, firms belonging to an industrial conglomerate; (iv) institution, such as banks and insurance companies, and foreign owners. We expect these different types of ownership to be char-acterized by different degrees of relevance of personal relationships. For instance, own-ers of family business are likely to derive utility from controlling the firm above and be-yond the pure monetary returns. Part of these returns might come from a compliant entourage and/or a group of executives who pursue the prestige of the family. A politi-cian (the “owner” of a government-controlled firm) might want executives who serve his political interests and might care little about how efficiently the firm is run. We therefore expect these types of firms to be characterize by positive values of R. Firms controlled by other entities, such as a foreign institution or a conglomerate, are instead more likely to put weight on pure monetary returns.14Independently from these presumptions, in the estimation exercise we will not impose any restriction on the values of R and will let the data speak.
Table1reports summary statistics for the firm data used in the regression analysis both for the total sample and by control type. For the total sample, on average, firms have value added of 30 million euros (at 1995 prices) and employ 691 workers, of which 13are executives. The average ratio of executives to total workforce is 26%. Around 41% of firms are classified as medium high and high tech according to the Organization for Economic Cooperation and Development (OECD) (2003) system, and 75% are located in the north. Clear differences emerge according to the control type. Family firms are substantially smaller than the average (11 million euros and less than 300 employees) and specialize in more traditional activities. Importantly, they have a lower TFP level, followed by government-controlled firms, while foreign firms have the highest TFP.
14We lump institutional and foreign owners together because both ownership types are not likely to be
identifiable with a single individual, so that from our perspective, it makes sense to assume a common R. Moreover, these two types by themselves have substantially fewer observations than family or conglomerate firms (see Table1), making inference less reliable. We have experimented with five categories, distinguish-ing between foreign and institutions, finddistinguish-ing similar (although less precise) results.
Table 1. Descriptive statistics: firms’ characteristics by control type.
VA Empl. No. Exec. %Exec. TFP %High Tech %North No. Obs. No. Firms All firms Mean 300 692 133 0026 241 041 074 7773 802 S.D. 1273 3299 291 0021 051 049 044 Family Mean 112 281 57 0024 233 033 073 2906 349 S.D. 180 420 98 0016 046 047 044 Conglomerate Mean 445 1024 150 0026 244 040 082 2390 300 S.D. 2142 5637 275 0025 054 049 039 Government Mean 406 1013 218 0022 238 047 051 687 99 S.D. 874 2076 575 0021 061 050 050 Foreign Mean 370 791 198 0030 253 052 075 1790 274 S.D. 691 1563 329 0022 048 050 044
Note: The notation VA is value added (in millions of 1995 euros), No. Exec. is the number of executives, % Exec. is the share
of executives over the total number of employees, TFP is the log of total factor productivity, % High Tech is the share of firms classified as medium high and high tech according to the OECD classification system (OECD (2003)), % North is the share of firms located in the North, No. Obs. is the number of firm-year observations, and No. Firms is the number of unique firms observations.
The executives’ data are taken from the Istituto Nazionale della Previdenza Sociale (Social Security Institute (INPS)), which was asked to provide the complete work histo-ries of all workers who were ever employed in an INVIND firm over the period 1981– 1997. Workers are classified as blue collar (operai), white collar (impiegati), and exec-utives (dirigenti). The data on workers include age, gender, area where the employee works, occupational status, annual gross earnings, number of weeks worked, and the firm identifier. We only use workers classified as executives. In our preferred specifica-tion, an executive turns senior after 5 years of tenure. Table2reports the statistics on executives’ characteristics for the total sample and by control type. For the total sample, average gross weekly earnings at 1995 constant prices are 1236 euros, and the share of executives who have been with the firm at least 5 years is 057 and at least 7 years is 045. Executives are, on average, 465 years old and 96% are male. Family-controlled firms pay lower wages to their executives and have a higher share of senior executives (62%). Ex-ecutives’ characteristics at conglomerate-controlled firms are fairly similar to the overall ones. Government-controlled firms employ older and almost exclusively male execu-tives. Finally, foreign-controlled firms pay their executives more, while their executives’ characteristics resemble the average in terms of the tenure, age, and gender composi-tion.
5. Identification
This section discusses the mapping between the model and the data, and, in particular, the data variability that identifies the model’s parameters. We first show that the model
Table 2. Descriptive statistics: executives’ characteristics by control type.
Wage φ5 φ7 Age %Male
All Firms Mean 1236 057 045 465 096 S.D. 330 030 031 46 013 Family Mean 1130 062 051 460 094 S.D. 288 033 033 53 017 Conglomerate Mean 1294 053 041 466 097 S.D. 321 028 028 40 009 Government Mean 1298 054 042 477 099 S.D. 349 027 027 46 003 Foreign Mean 1309 054 043 469 096 S.D. 361 029 029 41 012
Note: Wage (gross, per week) is in 1995 euros; φ5is the share of executives with at least 5 years of seniority, and φ7is the
share with at least 7 years. Age is the average executives’ age and % Male is the share of male executives.
yields a restriction that has a natural interpretation in terms of an OLS regression run over a cross section of firms of a given ownership type. This regression identifies a sub-set of the model’s parameters, while allowing to control for several unobserved variables that are not accounted for by our theory. We then show that more structural param-eters can be identified by comparing the average X, φ values across ownership types. These two sets of estimates exploit completely different dimensions of data variability. The results, therefore, can be compared to gain some insights on the consistency of our findings.
The model yields a simple prediction on the productivity differential between the se-nior and the juse-nior executives within a given ownership type. Fix R, q and consider a set of firms drawn from a given model parametrization. Firm i employs niexecutives. Those firms differ with respect to the quality of executives, which depends on the realizations of x+ r for each executive. The econometrician observes the firm’s productivity Xiand the fraction of senior executives φi, where the mean productivity of firm i is given by Xi=
ni j=1xij
ni , and the fraction of senior executives is φi= ni
j=1Iij
ni where,Iij is an indi-cator function equal to 1 if executive j in firm i is senior. Let Xoand Xy= μ be the large sample conditional productivity of the incumbent senior and junior executives, respec-tively. If niis not large, the average productivity will differ from Xo, Xydue to sampling variability. Using equation (6), we establish the following proposition.
Proposition 3. The productivity of firm i can be written as
Xi= μ + (Xo− μ)φi+ εi (8)
A key result from this proposition is that deviations εiabout the (large sample or unconditional) mean values are uncorrelated with the share of senior executives φi. In-tuitively, this property holds since an increase (or a decrease) in the quota of senior ex-ecutives φi about its unconditional mean φ does not contain any information on the innovation εi, that is, the amount by which the productivity of the senior (junior) exec-utive exceeds the selection threshold s∗ in firm i. From a statistical point of view, this result is an immediate corollary of the properties of the conditional mean. The propo-sition implies that the productivity differential Xo− μ can be estimated with an OLS regression of Xion φi. The intuition is the following. When selection is weak (i.e., R is large), two firms with different shares of senior executives differ little in productivity, since, on average, senior executives are not much more productive than junior execu-tives. This implies that the correlation between X and φ is low. If R is low, the selection mechanism is effective, senior executives are, on average, more productive than junior ones, and differences in φ will go together with substantial differences in X, yielding a high correlation between X and φ.
Another prediction of the model concerns a comparison across ownership types. Consider the firm productivity X and the fraction of senior executives φ. For a given vector of model primitives β, ρ, G(·), Figure3shows that for each admissible (i.e., model generated) observable pair X, φ, there is at most one pair of parameter values R, q that can produce it. Each line in the figure is indexed by one value of q. Increasing q shifts the locus upward: a higher probability of maturing a valuable relationship increases the like-lihood of being tenured and hence φ. Notice that all lines depart from the same point in the X, φ plane, which corresponds to R= 0. This is the productivity maximizing situa-tion, obtained when relationships have no value. Starting from this point, an increase in Rmoves the model outcomes along one line (indexed by q) from right to left. We know
Figure 3. Productivity and seniority: space spanned by the model. Note: The figure uses the parameters β= 098 (per year) and ρ = 011 (per year); G(·) is log normal with log mean λm= 16 and log std λσ= 036, which imply that log(μ) = 167.
this because, as shown in Proposition2, X is decreasing in R. Moreover, as discussed above, the effect of an increase in R on φ is, in general, not monotone. This explains why the lines that correspond to low values of q are hump-shaped. The important point of this figure is that those lines never cross, so that given any point in the space spanned by the model, one can invert it and retrieve the values of q and R that produced it.
Compared to this structural estimate, the regression of Proposition3only identifies the productivity differential Xo− μ, and not the levels of R, q. The two approaches to estimating the model that we discussed above are useful for a number of reasons. First, they allow us to assess one key prediction of the model using different moments from the data: while the structural estimates use the average values of X, φ of a given con-trol type to back out the R, q parameters across types, the OLS regression exploits the partial correlation coefficient between X and φ across firms for a given R, q. The lat-ter estimate does not depend on the average X, φ for a given control type, but on how X and φ covary across firms of a given type. This implies that the OLS estimates are robust to potential differences in either TFP or seniority structure that, on average, af-fect all firms in a control type equally. For example, one might argue that due to career considerations, foreign-controlled firms are uniformly more appealing to junior execu-tives than the other types. This would affect the structural estimates through changes in the average φ across control types unrelated to R, but would not bias the OLS esti-mates. A second important feature of the OLS estimates is that they do not require one to pin down all the structural parameters. In particular, they are independent of (and, of course, do not supply any information on) β, q, ρ, and G(·). They therefore offer a test of robustness of the structural estimates with respect to the values of the auxiliary parameters they hinge on. Finally, within a regression framework it is easy to perform robustness analysis, something that we exploit in the next section.
6. Model-based OLS regressions
This section presents various estimates of the model predictions discussed in Proposi-tion3. After presenting the baseline estimates, we analyze their robustness and discuss alternative hypotheses for interpreting the data.
6.1 Basic framework and results
Equation (8) establishes a relationship between the share of senior executives and firm-level TFP that we use to construct an OLS-based estimate of the productivity differential between senior and junior executives. By taking the log of both sides and applying a first order Taylor expansion around Xi= μ, we obtain
log Xi= γ0+ γ1φi+ ηi (9)
with γ0= log μ, γ1= Xoμ−μ, and ηi= μ1εi, and where, as shown in Proposition3, εi is uncorrelated with φi. This equation shows that in a regression of log TFP on the share of senior executives, the coefficient γ1 measures the percentage difference in average
ability between senior and junior executives. We bring equation (9) to the data using the specification
logTFPit= γ0+ γ1φit+ γfamDfam· φit+ γgovDgov· φit+ γforDfor· φit + γ5Wit+ ηit
where the dummies Dkwith k= (fam gov for) are control status dummies equal to 1 for family-, government-, and foreign-controlled firms, respectively, and Witis a vector of controls that includes year dummies, two-digit sector dummies, and control-status dummies that account for potential unobserved heterogeneity across firms with differ-ent control types. The coefficidiffer-ent γ1measures the percentage difference in the average ability of senior and junior executives in conglomerate-controlled firms, the reference group in this specification. Under our assumption that the productivity of junior execu-tives is the same across groups, the coefficients γkmeasure the difference in the average ability of senior executives for the corresponding control type with respect to the con-glomerate firms: γk= Xo(Rk)− Xo(Rcong). To obtain population consistent estimates, we weight observations with population weights, available from the INVIND survey, un-less otherwise specified.
The estimates reported in column (1) of Table3show that the relationship between productivity and the share of senior executives is positive for conglomerate-controlled firms: the coefficient is 011 with a standard error of 004. The positive sign of this coeffi-cient is consistent with the selection hypothesis, that is, with the assumption that senior executives are, on average, more productive than junior ones. To give a sense of the size
Table 3. TFP and share of senior executive relationship by control type. Dependent Variable: log TFP
(1) (2) (3) (4) (5) (6) φ 011∗∗∗ 002 008∗ 009∗∗ 011∗∗ 012∗∗∗ (004) (003) (004) (004) (004) (004) φ· foreign −003 001 002 −005 002 −002 (006) (005) (007) (006) (007) (007) φ· family −017∗∗∗ −010∗∗ −017∗∗∗ −013∗∗ −011∗∗ −013∗∗ (005) (004) (005) (005) (005) (005) φ· government −047∗∗∗ −032∗∗∗ −042∗∗∗ −037∗∗∗ −034∗∗∗ −029∗∗ (009) (007) (011) (009) (011) (012) Observations 5875 5943 4897 6840 5136 5136 R-squared 047 049 045 047 053 054
Note: The variable φ is the share of senior executives who have been with the firm at least 5 years in columns (1), (2), (5),
and (6), at least 7 years in column (3), and at least 3 years in column (4). All regressions are weighted with sampling weights with the exception of column (2), which is unweighted. All regressions include control type dummies, year dummies, and two-digit sector dummies. Column (5) also includes firm size (log of the number of employees), firm age (log), the average age of the workforce (log), and the share of executives, of white collar workers, and of male workers as a fraction of the total workforce. Column (6) includes the same additional controls as in column (5) interacted with ownership dummies. Robust standard errors are given in parentheses. Significance levels for the null hypothesis of a zero coefficient are labelled with asterisks:∗is 10%,
of the effect, the productivity of a firm with a share of executives that is 1 standard devi-ation above the mean (see Table2) is higher by about 3%. The estimated coefficient for the foreign-controlled firms, γforis not statistically different from zero; hence, we can-not reject the hypothesis that the selection in foreign-controlled firms is similar to that in conglomerate-controlled firms at conventional levels of significance. Instead, selec-tion appears to be significantly smaller in family firms, where senior executives are, on average, 17% less productive than in conglomerate-controlled firms. Finally, we obtain a very large negative coefficient for government firms (−047). This value implies a neg-ative selection in such firms, that is, that junior executives are more efficient than senior ones, an outcome that our model cannot predict (the worst selection we can have in the model makes the productivity of the senior executives equal to that of the junior). This indicates that government firms display some features that the model cannot match, an issue that will also arise in the structural estimates of Section7. Altogether, the sign and magnitude of the effect is indicative of very poor selection in government-controlled firms.
As a first robustness check, in column (2) we do not weight observations. In this case, the results are somehow weaker: the coefficient on φ is positive but statistically insignificant. The interaction terms for family and government are negative and signif-icant, again pointing to weaker selection in these firms. Another important issue is the length of time assumed necessary to become senior, which is 5 years in the baseline re-gressions. It is important to check to what extent our results depend on this choice. To do so, in column (3), we use a 7-year-based definition of seniority, and in column (4), we use a 3-year definition. We find no substantial differences with respect to the basic specification.
6.2 Additional robustness checks and alternative hypotheses
This section discusses potential criticisms of the regressions reported above to further assess their robustness. A first criticism of the regression analysis may concern an omit-ted variable bias. Our stylized theoretical model excludes other potential determinants of seniority and productivity. For example, a firm with a good human resource (HR) de-partment might be more productive and better at retaining senior managers. Formally, let Zimeasure the quality of the HR department and assume that the correct regression equation is
log Xi= γ0+ γ1φi+ γ2Zi+ ηi
Then the estimated coefficient on seniority using (9) would be equal to ˆγ1 = γ1+ γ2cov(φvar(φiZi)i). The omitted variable hypothesis might thus offer an alternative explana-tion of the correlaexplana-tion between seniority (φ) and productivity (X) that we found within each ownership type. But notice that while this bias might explain the presence of a positive correlation between productivity and seniority, more assumptions are neces-sary to challenge our main finding, namely that ˆγ1 differs across control types in the way predicted by our theory. In particular, to reproduce our finding that the conditional correlation between X and φ is high in firms under conglomerate control and is small
in family firms requires us to assume much more than an omitted variable, namely that either γ2or cov(φi Zi)/var(φi)differs systematically across ownership types. Following up on the above example, one would need a theory that explains why the quality of the HR department has a different impact on productivity and/or on the seniority structure in, for example, family with respect to conglomerate firms. To challenge our identifica-tion mechanism one needs an alternative theory of why the effect of an omitted variable varies across control types. We were unable to identify any obvious alternative explana-tion in the literature.
Despite this important theoretical objection, we further explore the role of omitted variables empirically, as our data base contains a rich set of firm characteristics, partic-ularly on the workforce composition, owing to the matched employer–employee nature of the data. Rather than trying to propose and dismiss a specific hypothesis, we select a set of potential determinants of productivity and include them in the regression. In col-umn (5) of Table3we report the results when including, as additional controls, firm size (log of the number of employees), firm age, the average age of the workforce, and the share of executives, of white collar workers, and of male workers as a fraction of the total workforce. To save on space, we report the coefficients on these additional controls in Table9in AppendixD. Even with this very rich set of controls, the pattern that emerges from the data is unchanged: the share of senior executives is positively correlated with TFP in conglomerate- and foreign-controlled firms, while it is significantly lower in the other two types.
A potential criticism of the specification of column (5) is that we are giving the share of senior executives a better chance to affect the results than to the other controls, since the coefficient of the seniority share varies by control type while those of the additional controls do not. We relax this restriction in column (6), where all the additional regres-sors listed above are interacted with the control type dummies. Again, the results are hardly affected. Interestingly, the interaction between the additional controls and the ownership type dummies are almost all insignificantly different from zero (Table9in Appendix D), suggesting that the differential response we find for the share of senior managers is not a general feature of the data.
One might still argue that only exogenous variation in φ can conclusively dismiss omitted variable bias (as well as any other endogeneity concern). We argue that this is not the case. The estimates of the productivity differential, Xo− μ, are based on the model predicted correlation between the share of senior managers and productivity, and do not reflect a generic form of causation from seniority to productivity. In fact, changes in φ that are not attributable to the selection mechanism will not identify Xo− μ. For example, an exogenous increase in the share of senior managers derived from a tighten-ing of labor market regulation that makes firtighten-ing more costly would reduce the selection and weaken the seniority–productivity correlation.15In other words, the interpretation of our estimate is the correct one under our maintained assumption that the theoretical model is the data generating process. In this sense, the estimates are structural, and the OLS correlation, as opposed to instrumental variable estimation, is the proper way to measure selection consistently with our model.
As a final set of robustness checks, we have experimented with the measure of per-formance. We have estimated the production function directly, rather than using the two-step procedure that first estimates TFP and then relates it to the share of senior ex-ecutives. The results are reported and discussed in AppendixD. They are aligned with those of Table3. We have also used profit-based measures of performance, as profits might capture different dimensions of managerial ability.16The results using return on assets (ROA) are reported in Table4. In this case, the coefficient on the share of senior ex-ecutives can be interpreted as the difference in the average contribution to ROA of senior and junior executives. The patterns we find are exactly the same as those that emerge when the productivity measure is used; if anything, they are stronger. In particular, prof-itability is positively related to the share of senior executives in conglomerate-controlled firms.17The interaction for foreign firms is not significantly different from zero, while it is negative and significant for family and government firms. Again, for the latter, the ef-fect is very strong, indicating negative selection in such firms. This is fully consistent with the results obtained when performance is measured by TFP. In particular, in fam-ily and government firms, the selection effect for senior executives is absent compared
Table 4. ROA and share of senior executives by control type. Dependent Variable: ROA
(1) (2) (3) (4) (5) (6) φ 340∗∗∗ 293∗∗∗ 230∗∗∗ 322∗∗∗ 395∗∗∗ 401∗∗∗ (075) (066) (085) (074) (086) (086) φ· foreign −157 024 −092 −071 032 034 (138) (107) (135) (136) (160) (165) φ· family −448∗∗∗ −369∗∗∗ −332∗∗∗ −425∗∗∗ −388∗∗∗ −405∗∗∗ (095) (078) (107) (096) (105) (105) φ· government −750∗∗∗ −373∗∗ −471∗∗ −722∗∗∗ −582∗∗∗ −595∗∗ (161) (150) (184) (167) (211) (232) Observations 5875 5943 4897 6840 5136 5136 R-squared 008 009 008 008 012 013
Note: ROA is return on assets, in percentage units; φ is the share of senior executives who have been with the firm at least
5years in columns (1), (2), (5), and (6), at least 7 years in column (3), and at least 3 years in column (4). All regressions are weighted with sampling weights with the exception of column (2), which is unweighted. All regressions include control type dummies, year dummies, and two-digit sector dummies. Column (5) also includes firm size (log of the number of employees), firm age (log), the average age of the workforce (log), and the share of executives, of white collar workers, and of male workers as a fraction of the total workforce. Column (6) includes the same additional controls as in column (5) interacted with ownership dummies. Robust standard errors in given in parentheses. Significance levels for the null hypothesis of a zero coefficient are labelled by asterisks:∗is 10%,∗∗is 5%, and∗∗∗is 1%.
16Foster, Haltiwanger, and Syverson (2008)showed that efficiency and profitability might not be simply
one-to-one.Sraer and Thesmar (2007)showed that family firms in France pay lower wages in exchange for more job security. Owners of family firms might, therefore, attract lower quality, higher risk-averse execu-tives and pay them less. In principle, family firms might, therefore, be both less efficient and more prof-itable.
17To get a sense of the size of the estimated effect, considering a firm whose share of senior executives
increases by 1 standard deviation above the mean (see Table2) would increase ROA by 1 percentage point (the median ROA is 78; the mean is 86).
to the other control types. Moreover, the results are robust to all the additional checks performed for TFP, reported in columns (2)–(6). Similar results are obtained when using return on equity (not reported for brevity). This shows that our results are robust with respect to different performance measures.
To conclude, the OLS estimates indicate that there are substantial differences in the effectiveness of the selection process of executives across different types of owners. We have argued that such differences are not likely to be due to omitted variable bias or to one specific performance indicator. We now turn to the structural estimation exercise, which will allow us to check if these conclusions are confirmed and to assess the effects of the private benefits from personal relationships on firms’ productivity through coun-terfactual exercises.
7. Estimates of the structural parameters
This section presents the structural estimation of the model parameters. We begin by discussing the assumptions needed for identification using firm-level observations on TFP and seniority of the executives, which we see as empirical measures of Xiand φi, that is, the observed productivity and share of senior executives in firm i. A third observ-able used for the estimation is the variance of the regression residual in equation (9), which we label var(ηi).
The estimation is developed under the assumption of observed heterogeneity, as some structural parameters are linked to observable characteristics of the firm, along the lines ofAlvarez and Lippi (2009). The distribution of productivity G(x) is assumed to be log normal, so that the model is characterized by six fundamental parameters: the discount factor β, the hazard rate ρ, the log normal parameters λmand λσ(log mean and log standard deviation, respectively), the probability of developing a relationship, q, and the value of the relationship R. Five parameters, namely β, ρ, q, λσ, and λm, are assumed to be common to all firms. The parameter R is assumed to vary with one observable characteristic of the firm: the control type. Given a parametrization (i.e., the vector β, ρ, q, λσ, λm, R), the model uniquely determines the values of X, φ, and var(η) to be observed in the data. In the estimation procedure, the differences between data points with identical observables (e.g., two firms with the same control type) are accounted for by classical measurement error. Next, we fill in the details that relate to the data used in the estimation, and describe the estimation algorithm and the results.
Our parsimonious structural estimates concern seven parameters: θp∈ Θ71, p= 1 2 7, described next. The firm-level observations vary across 14 years (index t), 13 two-digit sectors (index τ), and four control types described in the previous section (in-dex κ). We assume that R varies across firms according to the nature of the controlling stakeholder, with Rκ= θκ, κ= 1 2 3 4, for the firms with control type family (θ1), con-glomerate (θ2), government (θ3), and foreign (θ4), respectively. The parameter λm= θ5 measures the mean (log) TFP of the firm. In the data, TFP has a clear time component as well as a sectoral one, which are ignored by the simple structure of our model. Thus, be-fore turning to the structural estimation, we normalize the TFP data by removing
com-mon time and sector effects. Our measure of X for firm i in year t and sector τ is thus given by
log Xitτ≡ log TFPitτ− a1· yearit− a2· sectiτ− a3· Zitτ (10) where a1and a2are the vectors of coefficients from an OLS regression of TFP on 13 year and 12 two-digit sector dummies. We also consider a specification that controls for the effect of firm size Zitτ(log employment) on TFP. The parameter θ6measures the prob-ability of developing a relationship q= θ6
1+θ6. The parameter θ7measures the standard deviation of the ability distribution (see AppendixCfor a discussion of the mapping be-tween this parameter and the observable regression squared error var(ηi)).
To reduce the computational burden, two parameters are pinned down outside the estimation routine. The time discount β is calibrated to an annual value of 098, as is standard in the literature. The hazard rate of senior executives, ρ, is computed from the survival function of senior executives, that is, with at least 5 years of seniority, using the Kaplan and Meier (1958)estimator on the individual data. We estimate ρ= 011 per year, which implies that the expected tenure of senior executives is approximately 10 years.
These assumptions imply that after removing time and sectoral differences, all firms in a group—indexed by the control type κ= 1 2 3 4—are expected to have the same X and φ. For each firm i in group κ, there are two observables yiκj , j= 1 2. We assume that the variable yiκj is measured with error eji that is normal, with zero mean, inde-pendent across variables, groups, and observations. Inspection of the raw data suggests that measurement error is multiplicative in levels for TFP, X, and additive for the share of senior executives, φ.18 Hence the maximum likelihood (ML) estimates use the ob-servables yiκ1 = log Xiκand yiκ2 = φiκ. The measurement error variance σj2, j= 1 2, is assumed common across groups, and is computed as the variance of the residuals of an OLS regression of log X and φ on year and sector dummies. This gives σlog X2 = 035 and σφ2= 029. Finally, for each control group κ, we use the variance of the regression resid-ual in equation (9) as the third observable, yκ3= var(η), to be fitted by the model for each group.
Let fj(Θ κ)be the model prediction for the jth variable in group κ under the pa-rameter setting Θ. The observation for the corresponding variable for firm i in group κ is
yiκj = fj(Θ κ)+ eji
Let Y be the vector of observations and let nκbe the number of firms i in group κ. Define the objective function F as
F(Θ; Y ) ≡ 4 κ=1 3 j=1 nκ σj2 1 nκ nκ i=1 yiκj − fj(Θ κ) 2 (11)
18This statement is based on an analysis of the deviations of X and φ (in levels and in logs) from the
Table 5. Structural estimates of model parameters.
q Rfam Rcong Rgov Rfor λm λσ
A. Baseline 078 55 33 60 35 159 039
(25) (86) (101) (63) (103) (769) (309)
B. With firm size 076 51 34 69 35 159 040
(25) (88) (102) (43) (99) (744) (305)
Note: The t-statistics are given in parentheses. The estimation uses the estimated measurement errors σlog X2 = 035 and σ2φ= 029. The parameters β and ρ are calibrated (see the main text). The measure for productivity log X is the firm-level (log) TFP net of the common components due to year effects and sector effects, as from equation (10) (see the main text); in specification B, firm-size effects (as measured by the (log) number of employees) are also controlled for.
AppendixEshows that the likelihood function is related to the objective function by
log L(Θ; Y ) = −1 2 4 κ=1 3 j=1 nκ1+ log2πσj2 −1 2F(Θ; Y )
We estimate the structural parameters in Θ by minimizing (11). At each iteration, the algorithm solves the model for each of the four groups and computes the objective func-tion under the candidate parametrizafunc-tion. Since each group has three observables, there is a total of 12 moments to be fitted using 7 parameters; hence, the model is overiden-tified with 5 degrees of freedom. The formulas for the score and the information matrix used for the inference are derived in AppendixE.
The estimates of the model structural parameters are reported in Table5. The esti-mated value of q= 078 indicates that approximately 75% of the executives develop a relationship. The value of R varies substantially across control types, but all types en-joy some degree of private benefits: R is always significantly different from zero. This is consistent with the findings ofTaylor (2010), according to which CEO entrenchment is substantial even in U.S. listed firms, where family and government firms play a minor role. The importance of the relationships is lowest for firms that belong to a conglomer-ate (33), followed by foreign-controlled firms (35), family (55), and government (60). Given that the estimated unconditional mean level of TFP is around 7, the estimated values for R show that the nonmonetary characteristics of the executives (i.e., their rela-tionship value) are quantitatively important in the selection process.
To help with the interpretation of the structural estimates, Table6computes selected statistics produced by the model in the steady state at the estimated parameters. The first column solves the model for the (counterfactual) case in which the firm’s owner gives no value to relationships in executive selection (R= 0) and, hence, s∗= x∗for all senior executives. In this case, senior executives are confirmed if their ability x is above x∗= 62, which occurs in around 25% of cases. The (log) average ability of senior tives is 209, almost 30% higher than the unconditional average ability of junior execu-tives. On average, around 38% of executives are senior in this “frictionless” case. These figures can be compared to those obtained for family firms (second column of the ta-ble), for which s∗= 86 and x∗= s∗− R = 31 (the latter is the cutoff ability of executives
